3.3 Logarithmic Functions and Their Graphs

Logarithmic Functions The inverse of y = bx is y = logbx

Logarithmic Basic Properties logb 1 = 0 because b0 = 1 ex) log9 1 = logb b = 1 because b1 = b ex) log3 3 = logbby = y because by = by ex) log4 42 = blogbx = x because logb x = logb x ex) 7log73 =

You Try! Evaluate Each Expression log232 Log9√9 log644 5log517 log6(1/216)

Common Logarithms (Logs with base 10) log 1 = 0 because 100 = 1 log 10 = 1 because 101 = 10 Log 10y = y because 10y = 10y ex) log 1 = 1000 10log x = x because log x = log x ex) 10log(.5) =

Evaluate using calculator & Check log 9.43 ≈ Check: log (-14) = You Try! log 34.5 ≈ Check:

Solving Logarithmic Equations log x = 2 Log5 x = -3 You Try! log x = -1 Log4 x = 6

Natural Logarithms : Base e logex = ln x y = ln(x) is the inverse of the exponential function y = ex

Natural logarithms ln 1 = 0 because e0 = 1 ln e = 1 because e1 = e ln ey = y because ey = ey ex) ln e3 = elnx = x because ln x = ln x ex) eln 6 =

You Try! Evaluate: ln e -4 ln 1/e ln 4√e ln 4.05 ≈ Check:

g(x) = ln (x + 2) h(x) = ln (3 – x) g(x) = 3 log x h(x) = 1 + log x

Homework Pg. 308-309: 4, 10, 14, 22, 24, 26, 32, 36, 44, 58